Complete the square to solve for $x$. $2x^{2}+9x+4 = 0$
Solution: First, divide the polynomial by $2$ , the coefficient of the $x^2$ term. $x^2 + \dfrac{9}{2}x + 2 = 0$ Move the constant term to the right side of the equation. $x^2 + \dfrac{9}{2}x = -2$ We complete the square by taking half of the coefficient of our $x$ term, squaring it, and adding it to both sides of the equation. The coefficient of our $x$ term is $\dfrac{9}{2}$ , so half of it would be $\dfrac{9}{4}$ , and squaring it gives us ${\dfrac{81}{16}}$ $x^2 + \dfrac{9}{2}x { + \dfrac{81}{16}} = -2 { + \dfrac{81}{16}}$ We can now rewrite the left side of the equation as a squared term. $( x + \dfrac{9}{4} )^2 = \dfrac{49}{16}$ Take the square root of both sides. $x + \dfrac{9}{4} = \pm\dfrac{7}{4}$ Isolate $x$ to find the solution(s). $x = -\dfrac{9}{4}\pm\dfrac{7}{4}$ The solutions are: $x = -\dfrac{1}{2} \text{ or } x = -4$ We already found the completed square: $( x + \dfrac{9}{4} )^2 = \dfrac{49}{16}$